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Modeling Nanoscale Imaging in Electron Microscopy presents the recent advances that have been made using mathematical methods to resolve problems in microscopy. With improvements in hardware-based aberration software significantly expanding the nanoscale imaging capabilities of scanning transmission electron microscopes (STEM), these mathematical models can replace some labor intensive procedures used to operate and maintain STEMs. This book, the first in its field since 1998, will also cover such relevant concepts as superresolution techniques, special denoising methods, application of mathematical/statistical learning theory, and compressed sensing.

Integrated circuits -- Very large scale integration -- Design and construction. --- Metal oxide semiconductors, Complementary -- Design and construction. --- Nanoelectronics. --- Scanning transmission electron microscopy. --- Chemical & Materials Engineering --- Biology --- Health & Biological Sciences --- Engineering & Applied Sciences --- Microscopy --- Materials Science --- Electron microscopy. --- Nanoscale electronics --- Nanoscale molecular electronics --- Materials science. --- Analytical chemistry. --- Chemistry, Physical and theoretical. --- Physical measurements. --- Measurement. --- Nanotechnology. --- Materials Science. --- Characterization and Evaluation of Materials. --- Analytical Chemistry. --- Theoretical and Computational Chemistry. --- Measurement Science and Instrumentation. --- Molecular technology --- Nanoscale technology --- High technology --- Measuring --- Mensuration --- Mathematics --- Technology --- Metrology --- Physical measurements --- Measurements, Physical --- Mathematical physics --- Measurement --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Analysis, Chemical --- Analytical chemistry --- Chemical analysis --- Metallurgical analysis --- Mineralogy, Determinative --- Material science --- Physical sciences --- Electronics --- Nanotechnology --- Surfaces (Physics). --- Analytical biochemistry. --- Chemistry. --- Physics --- Surface chemistry --- Surfaces (Technology) --- Analytic biochemistry --- Biochemistry --- Chemistry, Analytic --- Bioanalytic chemistry --- Bioanalytical chemistry --- Measurement   . --- Analytic chemistry

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In April 2007, the  Deutsche Forschungsgemeinschaft (DFG) approved the  Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program.   Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance.  Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges.   Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program.   The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and, as such, they allowed us to use closely related approaches.  .

Differential equations. --- 517.91 Differential equations --- Differential equations --- Differential equations, partial. --- Mathematics. --- Computer science --- Numerical analysis. --- Distribution (Probability theory. --- Partial Differential Equations. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Numerical Analysis. --- Probability Theory and Stochastic Processes. --- Approximations and Expansions. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Partial differential equations --- Mathematics --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Probabilities. --- Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis